Ординатура / Офтальмология / Английские материалы / Handbook of Optical Coherence Tomography_Bouma, Tearney_2002

context of the optical imaging in scattering media. Section 11.3 describes the layouts that we have been exploring in our laboratory and the associated signal acquisition system. Section 11.4 is devoted to the performance of the full-field optical coherence microscopes in terms of resolution and sensitivity. Section 11.5 presents current applications of these systems.

11.2FULL-FIELD COHERENT IMAGING

In the development of many techniques, the first milestone has been to establish a point-to-point correspondence between a voxel located in the sample and a single detector. Acquisition of a 2-D or 3-D image data set then required scanning of either the probe or the sample. This was the case, for example, in magnetic resonance imaging (MRI) with a method known as the sensitive point method [14]. Nowadays this method is obsolete, for it has been replaced by direct 2-D or 3-D imaging of the sample [15]. As a matter of fact, if the power of the excitation source is not limited, parallel detection provides a clear improvement in acquisition time over a single-detector method, which we refer to here as the ‘‘multichannel advantage.’’ As a positive side effect, the minimization of moving parts also improves the stability and reproducibility of the images. In this section we outline some advantages of the head-on (XY) geometry in the context of OCT, we develop a comparison between single and multiple detectors, and we propose a way to perform a lock-in detection on an array detector.

11.2.1 Head-On (XY ) Geometry

Most current OCT systems are built around an XZ geometry (Z being the optical axis); they weakly focus the probe beam into the sample and take advantage of a rapid modulation of the reference arm. This geometry imposes a trade-off between lateral (X) resolution and the Z extent of the images [10,16]. Spatial resolution on the order of 10–15 m is usually achieved in these arrangements. A variant of OCT relying on an en face (XY) geometry, which includes the use of higher NA objective lenses and has been dubbed optical coherence microscopy (OCM) [10–12], can provide significantly higher resolution. In the case of systems using a full-field illumination and parallel detection, this geometry is the natural choice; this subsection outlines its specific advantages.

First, as mentioned above, optical coherence microscopy can take advantage of high NA objective lenses and produce images with high diffraction-limited resolution.

Second, in the XY geometry the acquisition time and the excitation power can be chosen according to the depth in the sample to compensate for the exponential attenuation of the excitation intensity with depth [17]. In contrast, a signal-to-noise ratio (SNR) degradation with depth is usually visible in XZ OCT scans, independent of the presence of multiple scattering effects. The use of a strongly focusing objective also allows delivery of a higher optical power to the sample surface when imaging deep within the sample. Indeed, the spread of the excitation beam being wider at the surface, less damage per unit of surface area is done than with an unfocused beam.

Third, the XY geometry makes it possible to naturally combine optical coherence imaging with complementary imaging modalities such as fluorescence [12].

Finally, in the specific case of full-field illumination, advantage can be taken of a spatially incoherent source to perform coherent detection without generating speckle in the whole image.

11.2.2 Serial vs. Parallel Detection

In this section we develop a comparison of the two detection schemes (single/multiple detector) in terms of acquisition time and signal-to-noise ratio (SNR), irrespective to the features common to all OCT arrangements.

In order to compare the two types of experiments (single and multiple detectors), we assume that the detector is not saturated and that the detection is shot noise limited. Coherent detection enables one to amplify the detected signal using a local oscillator (reference arm of the interferometer), and OCT setups usually achieve shot noise limited detection.

The classical expression of the signal-to-noise power ratio (SNRÞP for a single detector is [18]

where PS is the optical power received by the detector, is the frequency of the light,is the detector quantum efficiency, h is Planck’s constant, and B 1=2T is the measurement bandwidth (with T the acquisition time for one point) (Fig. 1).

Photodiodes and charge-coupled devices (CCDs) have similar light-to-electron conversion properties. For multiple detectors, the signal-to-noise power ratio expression is the same for each element of the M M matrix. Assuming that the available power is not limited and that a constant amount of energy can be delivered to every

point in the sample, a single-detector instrument requires a total time Ttotal ¼ M M T to obtain an M M image, whereas with a detector array the same image is

obtained in time T. In both cases, the voltage signal-to-noise ratio (SNR) can be expressed for each pixel of the image as

where T is the observation time for one pixel in the single-detector solution or for the whole M M matrix when an array of detectors is used.

We now define an efficiency criterion in order to take into account both SNR and total acquisition time:

The T factor in the above expression reflects the fact that averaging two acquisi- p

tions (thus doubling the acquisition time) improves the SNR by a factor of 2. We see that for a similar acquisition bandwidth and excitation power per pixel,

an M M detector array provides a gain of M in efficiency over a single detector (Table 1). This illustrates the ‘‘multichannel advantage’’ mentioned above.

Besides the signal-to-noise ratio, other issues must be pointed out.

a Power deposition, signal-to-noise ratio (SNR) and efficiency comparison between the singleand multiple-detector solutions. An M M matrix of detectors provides a net gain of M in efficiency compared to the single-detector scheme.

First, mechanical stability is easily ensured in the parallel detection scheme because there is only one slow mechanical translation, whereas in scanning systems fast movements along two directions may induce artifacts in the image due to vibrations. This may also degrade the reproducibility of the experiments and preclude SNR enhancement by ensemble averaging of several measurements.

Second, simultaneous acquisition of all the pixels of a given slice of the sample in one shot allows one to synchronize the acquisition of a complete image to a physiological event for certain in vivo studies.

In summary, a parallel (M M) detection scheme is attractive for the following reasons:

1.The mechanical translations and associated vibrations are reduced to a minimum.

2.Acquisition of all the pixels of an image is done simultaneously, yielding a good rejection of motion artifacts (sample motion, breathing, cardiac cycle, etc.) while allowing one to perform a stroboscopic acquisition synchronized on a physiological event (e.g., ECG).

3.The efficiency criterion is improved by a factor M as long as the detection is shot noise limited and the available source power is not limited. As a matter of fact, to fully benefit from the ‘‘multichannel advantage,’’ the source should allow delivery of the maximum acceptable amount of power simultaneously to all the pixels of the sample. At the present time, commonly available sources do not fulfil this requirement, especially if one is trying to obtain an en face image from deep within the sample, say close to the fundamental limits on OCT probing depth imposed by multiple scattering [19,20]. However, that concern might no

longer be an issue in the near future, conferring a net advantage to parallel detection schemes.

Before going any further, we need to define the principal requirements for an imaging array.

11.2.3 Solid-State Array Detectors

Three types of solid-state array detectors could be used in our application: silicon photodiode arrays (PDAs), CMOS image sensors, and charge-coupled devices (CCDs). The first solution is restricted to line (1-D) imaging because it is constituted of a linear array of photodiodes. CMOS image sensors are based on a bidimensional array of photodiodes. Each pixel also contains transistors to buffer and amplify the collected photocharge. The advantages of this design are the random readout of individual pixels and the use of standard CMOS technology, which enables low-cost volume productions. The main drawbacks are a low filling factor (i.e., the ratio of light-sensitive area to the total size of the pixel) of only 20– 30% and also poor linearity of the response. The last family, CCD sensors, have many applications, among which imaging is the most important. The basic light-to- electron conversion mechanism is the same as in photodiodes; the main difference is the collection (or integration) capability of these electrons in a CCD. The electric charges are stored in CMOS capacitors as in wells, and at regular time intervals these wells are emptied and the corresponding charge is transferred serially to the output of the device.

When comparing CCDs and photodiodes, the advantage of having a high number of elements on a CCD (from thousands to millions of pixels) is counterbalanced by the low frame rate of cameras and the limited storage capacity of each well, which limits their dynamic range. This storage capacity is designated as the full well capacity (FWC) of the CCD and is measured in electrons. (In most designs this capacity ranges from 50 ke to 400 ke .) This quantity is of impor-

SNR can be obtained in a time T essentially determined by the maximum pixel readout frequency Fpix of the camera: T ¼ M2=Fpix for an M M matrix. If we

can be measured continuously by the camera given the pixel readout frequency. Again, this supposes that the power limitation comes from the sensor, not from the light source, or from safety issues when irradiating tissues (e.g., maximum permissible exposure). To select a CCD for our application we must then maximize this criterion for a given image size.

Among the other parameters to consider when choosing a CCD camera, most important are the dark current that is generated by thermal activity in the sensor substrate (typical value 0.01 fA/pixel) and the readout noise due to the conditioning electronics (typically 10–20 electrons).

In summary, the selection of the best device is helped by the application of an efficiency criterion, but one must keep in mind that array detectors are slow (less than a few hundred images per second) compared to single detectors.

11.2.4 Parallel Coherent Detection

Optical Path Difference Modulation

In OCM, the useful signal to measure is usually very weak (i.e., interference between the local oscillator and the weak single-backscattered flux returning from the sample) compared to a large detected background due to reference flux and incoherent backscattered light. A usual remedy for such a situation is to extract the scarce information from the large unwanted signal by modulating the experiment at a given frequency while reading back the signal of interest through a lock-in detector (Fig. 2a). The signal is thus transposed at a frequency f0 by the modulation, where it can be extracted by multiplication with the reference signal at f0. This corresponds to a back transposition to a low frequency, where it is easy to minimize the noise by sharp low-pass filtering. This technique has numerous advantages. First, it greatly reduces the sensitivity of the experiment to temporal drifts and allows a precise match of the filter cutoff frequency to the useful bandwidth of the signal. Second, the modulation provides a great way to separate the useful information from the unwanted signal (background, background variations, EMI, etc.).

Applied to OCM, the lock-in detection method consists in modulating the optical pathlength difference between the arms of an interferometer. Thus, only the interference component is modulated in the detected flux, performing an effective discrimination of the coherent backscattered signal. The photoelastic modulator that we have been using to perform this modulation simultaneously in the whole image field is described in Section 11.3.3.

Multiplexed Lock-In Detection

Principle

The theoretical advantage of parallel detection was outlined in Section 11.2.2. We will now consider the main drawback of array detectors. Their low frame rate usually precludes the implementation of lock-in detection, thus canceling most of the potential advantages of parallel detection. As a matter of fact, conventional lock-in detection requires the multiplication of the signal sensor with the modulation reference. But, whereas photodiode bandwidths easily reach hundreds of megahertz (typical lock-in), CCD bandwidths are limited to approximately 1 kHz. Consequently the modulation frequency range allowed for lock-in experiments is reduced, which often precludes the use of lock-in detection with CCD detectors in physical experiments. For instance, our OCM experiments use a 50 kHz optical path difference modulation. At such frequencies, the temporal variations are averaged by the CCD cameras.

However, a way to have the benefit of the lock-in advantage is to modify the typical lock-in detection scheme (Fig. 2). Figure 2a shows the usual diagram, and Fig. 2b outlines the principle of our ‘‘multiplexed lock-in detection’’ method [13,21,22].

The ‘‘multiplexed lock-in detection’’ principle gets rid of the signal multiplication after the sensor (Fig. 2a) by using a secondary modulation. The latter performs the multiplication operation before the light signal reaches the sensor and is subsequently averaged. An example of secondary modulation is light modulation (e.g., light switching). Compared to typical lock-in detection, CCD exposure acts like a low-pass filter, and the integrating time constant is set by the CCD frame rate.

Figure 2 Typical lock-in detection versus multiplexed lock-in detection. The building blocks of the conventional detection scheme (a) are rearranged to get rid of slow array detectors (e.g., CCD) throughput (b).

Analytical Formulation

An analytical formulation of the ‘‘multiplexed lock-in’’ method that applies to any pixel of the CCD matrix is developed below.

Each pixel integrates the incident light flux ðtÞ during the CCD time exposure TFRAME. We note that S is the signal provided by the CCD camera:

ðTFRAME

0

The incident light flux results from the multiplication of the primary modulation function xT ðtÞ (reference) by the secondary modulation function yT ðtÞ. Both modulation functions are periodic of period T:

Assuming that the CCD exposure time is an integer number K of modulation periods, the signal S detected by the CCD is proportional to the cross-correlation

function xyð Þ of the xT ðtÞ and yT ðtÞ signals.

ðKT

Sð Þ ¼ xT ðtÞyT ðt þ Þ dt ¼ KT xyð Þ; with TFRAME ¼ KT ð7Þ

0

Since xT ðtÞ and yT ðtÞ are real and periodic, cross-correlation xyð Þ is also real and periodic. Its Fourier series gives the xT ðtÞ and yT ðtÞ cross-power spectrum.

Note that nF signifies that the cross-power spectrum is discrete (periodic signals). Expression (8) shows that the knowledge of one of the modulation functions

permits us to deduce the other:

Thus, sampling the cross-correlation function permits retrieval of the useful information present in the primary modulation.

In summary, a CCD camera integrates the light flux resulting from an ‘‘optical product’’ of two periodic time functions. The cross-correlation function is sampled by using an electronic device that also introduces delays between the two functions. Thus the acquisition process consists in grabbing several frames, each frame corresponding to a specific delay of the cross-correlation function. A linear combination of the acquired frames then gives access to the useful information about primary modulation. A detailed calculation for a specific example is presented in Section 11.3.4.

11.3FULL-FIELD OPTICAL COHERENCE MICROSCOPES

11.3.1 Possible Interferometer Geometries

In essence, full-field optical coherence microscopes are based on interference microscopes using low coherence optical sources. In a general manner, interference microscopes can be classified into two categories:

1.Interference microscopes in which the light returning from the object interferes with the light from a reference beam. These interference microscopes, involving two completely separated waves, are based on the Michelson interferometer principle (for observations in reflection) or Mach–Zehnder interferometer (for observations in transmission). These microscopes give the ‘‘normal’’ profile of the object.

2.Interference microscopes in which the image of the object is divided into two identical laterally shifted images that are made to interfere. In the case of small lateral shifts (of the order of the optical wavelength), the differential profile of the object is obtained (first spatial derivative of the ‘‘normal’’ profile). The Nomarski microscope is this kind of system.

In optical coherence microscopy, interference occurs between light backscattered by the object and light reflected by a reference mirror, the light being spatially and temporally incoherent. The analysis of the interference signal provides amplitude images (and possibly phase images) from specific regions in the object, where the interference fringes are localized. Different interferometer geometries can be used: ‘‘classical’’ Michelson [13] (Fig. 3a), Mirau [23] (Fig. 3b), and Linnik [24,25] (Fig. 3c). The drawback in the Michelson and Mirau configurations is that the

Figure 3 Geometries for Michelson-type optical coherence microscopes. (a) Michelson geometry; (b) Mirau geometry; and (c) Linnik geometry.

beamsplitter can introduce strong aberrations in wide-aperture systems, especially spherical aberration in the axial direction, which increases approximately as the cube of the numerical aperture. Because the reference and object beams share a common path over most of their length, this layout is less sensitive to vibrations than the Linnik configuration. In addition, only one lens is required, although this lens must have a relatively long working distance to accommodate the beamsplitter. The Linnik configuration requires two identical objectives, and because of the long beam paths involved it must be built massively to avoid vibration problems. Nevertheless, the great advantage of this configuration is that objectives with very high numerical apertures can be used (Fig. 3).

11.3.2 Light Sources

The light source used must fulfil several requirements.

1.Near-infrared wavelengths (typically between 700 and 1300 nm) are used to minimize scattering in tissues and achieve better penetration.

2.The temporal coherence should be as short as possible in order to avoid degradation of the effective resolution of the instrument when imaging in scattering media. In conventional optical coherence tomography, the axial resolution is principally defined by the coherence length of the source. In contrast, in optical coherence microscopy (OCM), when using a high NA objective lens, axial resolution is predominantly defined by the confocal nature of the signal detection. This is the case in our geometry, as detailed in Section 11.4.1. Nevertheless, the point spread function of the instrument is degraded when imaging deep within scattering media due to the detection of multiply scattered light. Reducing the coherence length of the source is a way to minimize these aberrations.

3.When full-field illumination is used, the spatial coherence of the source should be as low as possible in order to reduce speckle formation in the image.

4.Finally, to use the parallel coherent detection technique described in Section 11.2.4, the light source has to be modulated at a frequency of several kilohertz.

In practice, we use light-emitting diodes (LEDs) with typical output power of 40 mW at 840 nm and 20 nm full width at half maximum (FWHM) spectral bandwidth. The emitter size is 240 m 240 m. Light source modulation is achieved by directly modulating its driving voltage. We note that several such sources can be combined using a fiber-optic coupler to increase the spectral bandwidth [26].

11.3.3 Experimental Arrangement

Layout

We have developed in our laboratory optical coherence microscopes based on the Michelson [13] and Linnik [24] interferometer geometries, working with polarized light (Figs 4a and 4b, respectively). An infrared light-emitting diode (LED) is used as a spatially and temporally incoherent light source. Its spectrum is centered at ¼ 840 nm with FWHM 20 nm, i.e., a coherence length of 20 m. The spatially incoherent beam produced by the LED is linearly polarized and is separated by a polarizing beam splitter into two orthogonaly polarized beams. A polarizer placed after the LED makes it possible to control the balance of the relative intensities of the two beams. A photoelastic birefringent modulator (see next section) introduces a sinusoidal phase variation of amplitude and frequency f ¼ !=2 ¼ 50 kHz between the two orthogonal components, which are made to interfere by a second polarizer

Figure 4 Experimental arrangements of polarization coherence microscopes developed in our laboratory In these schematic representations, only one point of the object is imaged on the CCD camera array. Full-field illumination is used to generate parallel cross-sectional images. (a) Michelson geometry. A single objective (0.15 NA) is used to focus the light on the object and on a reference mirror using a polarizing beamsplitter cube. A 50% beamsplitter is used to image the object on the CCD camera array. This configuration is appropriate for low aperture microscope objective lenses. (b) Linnik geometry. Two identical objectives are used. Quarter-wave plates are inserted into the two arms to rotate by =2 the linear polarizations after reflection onto the reference mirror and by the object. The light reflected by the object is then totally transmitted by the polarizing beamsplitter whereas the light reflected by the reference mirror is totally reflected. Thus all the useful light is used. High numerical aperture objective lenses can be used.

oriented at 45 from the beam polarizations. The resulting image is finally detected on a two-dimensional CCD detector array.

Photoelastic Modulator

To introduce a stable periodic phase shift between the two orthogonal polarizations, we use a photoelastic birefringence modulator developed in our laboratory [27,28]. The device (Fig. 5) has a rectangular shape and is made of a transparent isotropic material (silica is well adapted for visible applications). A piezoelectric transducer (PZT) ceramic glued on its sides excites the system at its resonance frequency, introducing a periodic longitudinal stress that governs the induced birefringence. The driving voltage is low (a few volts) because we take advantage of the mechanical resonance (quality factor 100). The modulation frequency is given by

fm ¼ sound=2L, where sound is the speed of sound in the material and L is the modulator length. The PZT is usually glued at 1L=4 from one of the silica bar’s

edges (one of the two regions with maximum stress), while the other maximum stress region (3L=4 from the same edge) serves as the birefringence modulator. This minimizes residual birefringence induced by the glue.

Issues Raised by the Implementation

At this point, we wish to point out several issues that are raised by the full-field polarization layout described above.

First, we commonly use immersion objectives to reduce the refractive index mismatch between the sample and its surrounding medium. Index mismatch has two consequences that should be avoided. (1) It causes an important specular reflection at the sample surface that limits the amount of light that can be sent to the sample arm without saturating the detector, thereby limiting the effective detector dynamic range. (2) When focusing deep inside the sample, refractive index mismatch introduces an optical path difference between the interferometer arms. In the case of bulk Michelson geometry and nonimmersion objectives, a clever way to compensate for this walk-off has been demonstrated by Schmitt et al. [26]. Because this does not apply here, we try to minimize this effect by using an appropriate medium. In the Linnik geometry, the reference arm length can also be manually modified to compensate for the walk-off and the resulting loss of contrast.

Figure 5 Photoelastic modulator design. A transparent isotropic material is excited on its sides by a PZT ceramic.